{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Toy Problem - Traditional Approach\n",
    "\n",
    "In this tutorial, we'll simulate a simple 2D localization problem as per the figure below. We'll assume that we have a robot following a simple body-frame-velocity model, which has access to noisy measurements of its forward velocity $v$ and angular velocity $\\omega$. In addition, this robot will have a time-of-flight sensor that gives it range measurements to a few known landmarks in the environment. \n",
    "\n",
    "![Toy Problem](../toy_problem.png)\n",
    "\n",
    "\n",
    "## Define the State\n",
    "The first step is to define the state of the robot. We'll start with a more traditional approach and define the state of the robot to be a vector of the form $\\mathbf{x} = [\\theta, x, y ]^T$, where $x$ and $y$ are the robot's position in the world and $\\theta$ is its orientation. We'll also define the control inputs to be $\\mathbf{u} = [\\omega, v]^T$, the robot's forward and angular velocity. The process (motion) model of the robot is then given by:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "    \\dot{\\theta} &= \\omega,\\\\\n",
    "    \\dot{x} &= v \\cos(\\theta), \\\\\n",
    "    \\dot{y} &= v \\sin(\\theta). \n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "However, this is in continuous time, and we need to discretize it to use it in a filter. For now, we'll use the simple Euler discretization method, which gives us the following discrete-time process model:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "    \\theta_{k+1} &= \\theta_k + \\omega_k \\Delta t, \\\\\n",
    "    x_{k+1} &= x_k + v_k \\cos(\\theta_k) \\Delta t, \\\\\n",
    "    y_{k+1} &= y_k + v_k \\sin(\\theta_k) \\Delta t.\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "Lets now code up our state and process model using navlie's framework. Since our state is just a regular 3x1 vector, we can use a standard type from the built-in library: [navlie.lib.VectorState](../_autosummary/navlie.lib.states.VectorState.rst)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "VectorState(stamp=0.0, dof=3, state_id=None)\n",
      "    [0. 0. 0.]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "np.random.seed(0)\n",
    "import navlie as nav\n",
    "from navlie.lib import VectorState\n",
    "\n",
    "x = VectorState([0, 0, 0], stamp=0.0)\n",
    "print(x)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `VectorState` is a subclass of the abstract [State](../_autosummary/navlie.types.State.rst) class in navlie, which is one of the core primitive types. The value of the state is stored as a numpy array, and can be accessed directly through `x.value`. \n",
    "\n",
    "\n",
    "## Define the Process Model\n",
    "For the process model, we'll choose to define our own from scratch here. Process models in navlie *must* inherit from the abstract [navlie.ProcessModel](../_autosummary/navlie.types.ProcessModel.rst) class and implement the `evaluate` and either the `input_covariance` or `covariance` methods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from navlie.lib import VectorInput\n",
    "\n",
    "Q = np.eye(2) * 0.1**2 # Input noise covariance with 0.1 m/s of standard deviation\n",
    "\n",
    "class WheeledRobot(nav.ProcessModel):\n",
    "    def __init__(self, input_covariance):\n",
    "        self.Q = input_covariance\n",
    "\n",
    "    def evaluate(self, x: VectorState, u: VectorInput, dt: float) -> VectorState:\n",
    "        x_next = x.copy()\n",
    "        x_next.value[0] += u.value[0] * dt\n",
    "        x_next.value[1] += u.value[1] * dt * np.cos(x.value[0])\n",
    "        x_next.value[2] += u.value[1] * dt * np.sin(x.value[0])\n",
    "        return x_next\n",
    "\n",
    "    def input_covariance(self, x: VectorState, u: VectorInput, dt: float) -> np.ndarray:\n",
    "        return self.Q\n",
    "    \n",
    "process_model = WheeledRobot(Q) # instantiate it"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The methods in navlie process models must always accept the arguments shown above: a `State` object, an `Input` object, and a float `dt`. The `evaluate` method must always return a valid (i.e. subclass of a) `State` object, and the `input_covariance` method must always return a square numpy array. There are more optional methods that can be implemented for performance reasons, but we will cover those later.\n",
    "\n",
    "## Define the Measurement Model(s)\n",
    "Moving on to the measurement model, if $\\mathbf{r}_a = [x,y]^T$ denotes the position vector of the robot resolved in the world frame, and $\\mathbf{\\ell}^{(i)}_{a} \\in \\mathbb{R}^2$ is the 2 x 1 position vector of landmark $i$, then the measurement model for each landmark is simply \n",
    "\n",
    "$$ \n",
    "y_i = ||\\mathbf{r}_a - \\mathbf{\\ell}^{(i)}_{a}||\n",
    "$$\n",
    "\n",
    "In navlie, measurement models must be implemented in a similar way to process models: inherit from the [navlie.MeasurementModel](../_autosummary/navlie.types.MeasurementModel.rst) abstract class, and then implement the `evaluate` and `covariance` methods. Here's an example for this problem:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "class RangeToLandmark(nav.MeasurementModel):\n",
    "    def __init__(self, landmark_position: np.ndarray):\n",
    "        self.landmark_position = landmark_position\n",
    "\n",
    "    def evaluate(self, x: VectorState) -> np.ndarray:\n",
    "        return np.linalg.norm(x.value[1:] - self.landmark_position)\n",
    "    \n",
    "    def covariance(self, x: VectorState) -> np.ndarray:\n",
    "        return 0.1**2\n",
    "    \n",
    "landmarks = np.array([[1, 1], [1, 2], [2, 2], [2, 1]])\n",
    "meas_models = [RangeToLandmark(landmark) for landmark in landmarks]"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## (Simulation only) Generate fake data\n",
    "\n",
    "The next step is to generate some fake data for our simulation (although navlie is also compatible with real data). To do this, we will use the [DataGenerator](../_autosummary/navlie.datagen.DataGenerator.rst) class which is used as follows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "VectorState(stamp=0.0, dof=3, state_id=None)\n",
      "    [0. 0. 0.]\n",
      "VectorInput(stamp=0.0, state_id=None)\n",
      "    [0.4867558  0.40227221]\n",
      "Measurement(stamp=0.0, state_id=None) of RangeToLandmark\n",
      "    1.5906187969698615\n"
     ]
    }
   ],
   "source": [
    "dg = nav.DataGenerator(\n",
    "    process_model=process_model,                  # process model to use\n",
    "    input_func=lambda t, x: np.array([0.3, 0.5]), # a callable that specifies the input values over time\n",
    "    input_covariance= Q,                          # numpy array or callable that specifies the input covariance over time\n",
    "    input_freq=50,                                # the frequency (Hz) at which the input is sampled (and the process model integrated)\n",
    "    meas_model_list=meas_models,                  # a list of measurement models to use\n",
    "    meas_freq_list=[10, 10, 10, 10]               # corresponding measurement frequencies (Hz)\n",
    ")\n",
    "\n",
    "state_data, input_data, meas_data = dg.generate(x, start=0, stop=30, noise=True)\n",
    "\n",
    "print(state_data[0])\n",
    "print(input_data[0])\n",
    "print(meas_data[0])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The output of the `DataGenerator.generate` method is three lists: a list of ground-truth `State` objects, a list of `Input` objects, and a list of [Measurement](../_autosummary/navlie.types.Measurement.rst) objects, with the input/measurement lists possibly being corrupted by random noise if the `noise=True` flag is set. Each item in these lists correspond to different points in time. We can plot the trajectory as follows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Plot the state trajectory\n",
    "pos = np.array([state.value[1:] for state in state_data])\n",
    "plt.plot(pos[:, 0], pos[:, 1])\n",
    "plt.scatter(landmarks[:, 0], landmarks[:, 1])\n",
    "# add labels\n",
    "for i, landmark in enumerate(landmarks):\n",
    "    plt.annotate(f\"Landmark {i}\", landmark)\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.title(\"Simulated Trajectory\")\n",
    "plt.axis(\"equal\")\n",
    "\n",
    "\n",
    "# Plot the input data\n",
    "plt.figure()\n",
    "u_array = np.array([u.value for u in input_data])\n",
    "u_stamps = np.array([u.stamp for u in input_data])\n",
    "plt.plot(u_stamps, u_array[:, 0], label=\"omega\")\n",
    "plt.plot(u_stamps, u_array[:, 1], label=\"v\")\n",
    "plt.xlabel(\"Time (s)\")\n",
    "plt.ylabel(\"Input\")\n",
    "plt.title(\"Input Data\")\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Run a filter!\n",
    "\n",
    "Finally, lets run an extended Kalman filter on this data to get a state estimate that uses only the noisy measurements. In the below filter, we instantiate the [ExtendedKalmanFilter](../_autosummary/navlie.filters.ExtendedKalmanFilter.rst) to use on our data, and looping over the input measurements while also calling the correction step whenever a measurement occurs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# First, define the filter\n",
    "kalman_filter = nav.ExtendedKalmanFilter(process_model)\n",
    "\n",
    "# You can try other filters too!\n",
    "# kalman_filter = nav.UnscentedKalmanFilter(process_model)\n",
    "# kalman_filter = nav.IteratedKalmanFIlter(process_model)\n",
    "\n",
    "P0 = np.diag([0.1**2, 1**2, 1**2])  # Initial covariance\n",
    "x = nav.StateWithCovariance(x, P0)  # Estimate and covariance in one container\n",
    "\n",
    "meas_idx = 0\n",
    "y = meas_data[meas_idx]\n",
    "estimates = []\n",
    "for k in range(len(input_data) - 1):\n",
    "    u = input_data[k]\n",
    "\n",
    "    # Fuse any measurements that have occurred.\n",
    "    while y.stamp < input_data[k + 1].stamp and meas_idx < len(meas_data):\n",
    "        x = kalman_filter.correct(x, y, u)\n",
    "\n",
    "        # Load the next measurement\n",
    "        meas_idx += 1\n",
    "        if meas_idx < len(meas_data):\n",
    "            y = meas_data[meas_idx]\n",
    "\n",
    "    # Predict until the next input is available\n",
    "    dt = input_data[k + 1].stamp - x.state.stamp\n",
    "    x = kalman_filter.predict(x, u, dt)\n",
    "\n",
    "    estimates.append(x.copy())"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The filters in navlie are all designed to be *stateless*: this means that the actual state estimate is stored externally to the filter objects, in this case in a container called [StateWithCovariance](../_autosummary/navlie.types.StateWithCovariance.rst). Although this adds a slight burden on the user, it has the advantage of being more transparent, and also providing the ability to combine different filters in the same loop! For example, you could use an EKF for the prediction, but a UKF for the correction, or even to use different filters for different measurement models!\n",
    "\n",
    "\n",
    "Once estimates have been obtained, we will often be interested in evaluating the performance. The [GaussianResultList](../_autosummary/navlie.utils.GaussianResultList.rst) object is a useful container for evaluating the quality of the state estimates when ground truth data is available. It calculates useful metrics such as raw error, Mahalanobis distance, and normalized estimation error squared (NEES). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "results = nav.GaussianResultList.from_estimates(estimates, state_data)\n",
    "# results.nees \n",
    "# results.three_sigma\n",
    "# results.error\n",
    "# results.md # mahalanobis distance\n",
    "# # and more...\n",
    "\n",
    "# Some plotting functions that work directly with GaussianResultList\n",
    "fig, axs = nav.plot_error(results)\n",
    "axs[0].set_title(\"Estimation Errors\")\n",
    "axs[0].set_ylabel(\"theta (rad)\")\n",
    "axs[1].set_ylabel(\"x (m)\")\n",
    "axs[2].set_ylabel(\"y (m)\")\n",
    "axs[2].set_xlabel(\"Time (s)\")\n",
    "\n",
    "fig, ax = nav.plot_nees(results)\n",
    "ax.set_title(\"NEES\")\n",
    "ax.set_xlabel(\"Time (s)\")\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a final note, `GaussianResultList` will invoke the `State.minus` method of the state objects to calculate the error. As we will see next, this allows us to implement a custom measure of error, when it might not make sense to directly subtract two of our state objects."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.16"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
